Sine fits using fit_pandas_GUI()

You can try this notebook live by lauching it in Binder.This can take a while to launch, be patient. .

First we import pandas, numpy and pandas_GUI and then create some data to fit.

import pandas as pd
from pandas_GUI import *
import numpy as np
X = [k*np.pi/10 for k in range(-30,30)]
Y = 98*np.sin(X)+np.random.default_rng().normal(0,3,60)
df = pd.DataFrame({'X':X, 'Y':Y})

Default plot of the data set

This is the plot made using the default settings of plot_pandas_GUI(). See step-by-step example.

# CODE BLOCK generated using plot_pandas_GUI(). See https://github.com/JupyterPhysSciLab/jupyter_Pandas_GUI.
from plotly import graph_objects as go
Figure_1 = go.FigureWidget(layout_template="simple_white")
scat = go.Scatter(x = df['X'], y = df['Y'],
        mode = 'lines', name = 'Noisy Sine',)
Figure_1.add_trace(scat)
Figure_1.update_xaxes(title= 'Time')
Figure_1.update_yaxes(title= 'Amplitude')
Figure_1.update_layout(title = 'Noisy Sine Wave Default Plot', template = 'simple_white')
Figure_1.show()
# Force save widget states so that graph will still be
# available when notebook next opened in trusted state.
JPSLUtils.OTJS('Jupyter.actions.call("widgets:save-with-widgets");')

Figure 1: A plot of the noisy sine wave data. This should display a live plotly plot. If you are running a live notebook and do not see the plot make sure you have trusted the notebook (button near the kernel name and status).

Fit the data with a sine function

The fit was done by running the command fit_pandas_GUI() in an empty code cell.

1. On the first tab

the data set, which columns contained the X- and Y-data and a name for the trace were chosen.

2. On the second tab

the the default 'none' value was kept for uncertainties.

3. On the third tab

the SineModel was chosen and all the boxes were left in their default state.

4. The fourth tab was skipped

because we fit the whole range of data.

5. On the fifth tab

labels for the X and Y axis were input and the Display Mirror Axes box was checked.

6. On the last (sixth) tab

the final checks were done and then the 'Do Fit' button was clicked, closing the GUI and running the code in the cell below to perform the fit and display the results.

# CODE BLOCK generated using fit_pandas_GUI(). See https://github.com/JupyterPhysSciLab/jupyter_Pandas_GUI.
# Imports (no effect if already imported)
import numpy as np
import lmfit as lmfit
import round_using_error as rue
import copy as copy
from plotly import graph_objects as go
from IPython.display import HTML

# Define data and trace name
Xvals = df["X"]
Yvals = df["Y"]
tracename = "Noisy Sine"

# Define error (uncertainty)
Yerr = df["Y"]*0 + 1

# Define the fit model, initial guesses, and contraints
fitmod = lmfit.models.SineModel()
fitmod.set_param_hint("amplitude", vary = True, min = 0.0)
fitmod.set_param_hint("frequency", vary = True, min = 0.0)
fitmod.set_param_hint("shift", vary = True, min = -6.283195307179586, max = 6.283195307179586)

# Do fit
Fit_1 = fitmod.fit(Yvals, x=Xvals, weights = 1/Yerr, scale_covar = True, nan_policy = "omit")

# Calculate residuals (data - fit) because lmfit
#  does not calculate for all points under all conditions
resid = []
for i in range(0,len(Fit_1.data)):
    resid.append(Fit_1.data[i]-Fit_1.best_fit[i])

# Plot Results
Fit_1_Figure = go.FigureWidget(layout_template="simple_white")
Fit_1_Figure.update_layout(title = "Fit_1_Figure")
Fit_1_Figure.set_subplots(rows=2, cols=1, row_heights=[0.2,0.8], shared_xaxes=True)
scat = go.Scatter(y=resid,x=Xvals, mode="markers",name = "residuals")
Fit_1_Figure.update_yaxes(title = "Residuals", row=1, col=1, zeroline=True, zerolinecolor = "lightgrey", mirror = True)
Fit_1_Figure.update_xaxes(row=1, col=1, mirror = True)
Fit_1_Figure.add_trace(scat,col=1,row=1)
scat = go.Scatter(x=Xvals, y=Yvals, mode="markers", name=tracename)
Fit_1_Figure.add_trace(scat, col=1, row = 2)
Fit_1_Figure.update_yaxes(title = "Y", row=2, col=1, mirror = True)
Fit_1_Figure.update_xaxes(title = "X", row=2, col=1, mirror = True)
scat = go.Scatter(y=Fit_1.best_fit,x=Xvals, mode="lines", name="fit", line_color = "black", line_dash="solid")
Fit_1_Figure.add_trace(scat,col=1,row=2)
Fit_1_Figure.show()

# Display best fit equation
ampstr = ''
freqstr = ''
shiftstr = ''
for k in Fit_1.params.keys():
    if Fit_1.params[k].vary:
        paramstr = '(\color{red}{'+rue.latex_rndwitherr(Fit_1.params[k].value,
                                       Fit_1.params[k].stderr,
                                       errdig=1,lowmag=-3)+'})'
    else:
        paramstr = '\color{blue}{'+str(Fit_1.params[k].value)+'}'
    if k == 'amplitude':
        ampstr = paramstr
    if k == 'frequency':
        freqstr = paramstr
    if k == 'shift' and Fit_1.params[k].value != 0:
        shiftstr = ' + ' + paramstr
fitstr = r'$fit = '+ampstr + 'sin[' + freqstr + 'x' + shiftstr + ']$'
captionstr = '<p>Use the command <code>Fit_1</code> as the last line of a code cell for more details.</p>'
display(HTML(fitstr+captionstr))

$fit = (\color{red}{98.8\pm0.5})sin[(\color{red}{1.001\pm0.001})x + (\color{red}{0.006\pm0.006})]$

Use the command Fit_1 as the last line of a code cell for more details.

Figure 2: The results of fitting the noisy sine data to using default settings. Alternative formatting of line styles, markers, etc... can be accessed by editing the code produced by the GUI. Overall plot styling can be adjusted on tab 5.

Learn More

In addition to trying it below if this is a live notebook, you can look at the other examples listed in the Pandas GUI website.

Try It

If you are running this notebook live in binder you can try it here by running the first cell to import the tools and create the data. Then run the cell below to create the GUI. Note: You may want to expand the collapsed instructions to learn more about each tab.

fit_pandas_GUI()